Base62 Encoding

Base 62 is a positional number system using 62 distinct symbols. It allows for the representation of whole numbers using the 10 digits 0-9, the 26 uppercase letters A-Z, and the 26 lowercase letters a-z.

A commonly used alphabet is: 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz.

Base62 encoding involves performing a change of arithmetic base. The principle is as follows:

1 - Interpret the source data as an unsigned integer.

2 - Divide this integer successively by 62.

3 - After each division, keep the remainder (between 0 and 61) and assign it the corresponding character in the Base62 alphabet.

4 - Read the resulting characters in the reverse order of the divisions.

The correspondence between values and symbols depends on the chosen alphabet, which must be known during both encoding and decoding. Generally, the indices of the 62 symbols are:

Decoding a Base62 string involves reconstructing the represented integer and then potentially reinterpreting it as binary data.

The method is as follows: for a Base62 string of length $ n $, denoted $ c_0 c_1 \ldots c_{n-1} $ where $ c_0 $ is the leftmost character

1 - Assign to each character its numeric value $ v(c_i) $ between 0 and 61.

2 - Calculate the decimal value using the formula $$ \sum_{i=0}^{n-1} v(c_i) \times 62^{n-1-i} $$

The resulting number can then be converted to binary and decoded into ASCII or Unicode if necessary.

A Base62 string consists exclusively of the 62 alphanumeric characters: digits 0-9, uppercase letters A-Z, and lowercase letters a-z.

Base62 is case-sensitive: A and a represent distinct values.

It is likely that the distribution of the first few digits decoded can approximately follow Benford's Law.

Fun fact: Base62 is encoded as KixpUr22 and conversely, the string Base62 is equivalent to the number 169958929504, or the binary data 00100111,10010010,01010111,01110100,01100000

Base62 maximizes the use of characters available in most text environments (letters and numbers), allowing data to be represented more compactly than number systems based on smaller bases, such as Base 10 or Basis 16.

Base 62 allows data to be compacted, it is used in URL shorteners (web page addresses), in the generation of unique identifiers in computer systems, etc.

Base 62 is sometimes used to store numbers in character strings.